This book serves as a vital tool for researchers in Mathematics and related fields, addressing the need for a comprehensive resource on Distance. It emphasizes interdisciplinarity, accessibility, and applicability, featuring easy-to-locate definitions and structured content. Its aim is to bridge gaps between specialized areas without oversimplifying.
Focusing on their historical significance, Stirling numbers, introduced by James Stirling in 1730, are pivotal in Mathematics, particularly in Combinatorics and Algebra. They boast a rich history with deep connections across various mathematical fields, including arithmetic and number theory. The book explores their classical properties and highlights modern applications, showcasing the enduring relevance and versatility of these special numbers in mathematical research and practice.
Focusing on combinatorial mathematics, this book delves into Catalan numbers, exploring their historical context and diverse applications. It presents foundational concepts like recurrence equations, closed formulas, and generating functions, while also highlighting intriguing properties and number-theoretical aspects. The text further examines connections to related sequences, such as Bell and Motzkin numbers, and addresses ongoing open problems in the field. This comprehensive approach caters to both professionals and enthusiasts, offering insights into this fascinating area of mathematics.
Delving into the theory of perfect and amicable numbers, this book offers an in-depth exploration of two classes of special numbers, including their generalizations. It presents a comprehensive list of properties, facts, and theorems, complete with proofs. The text highlights the intriguing characteristics and historical significance of these numbers, showcasing their relevance in both classical and modern mathematics, as well as their connections to renowned mathematicians throughout history.
Focusing on two classes of special numbers, the book delves into their connection to classical problems in the Theory of Primes. It provides a comprehensive examination of these numbers, along with in-depth discussions on their applications in Cryptography, highlighting their relevance in modern security techniques.
The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the Goldberg–Coxeter construction for those graphs. It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians.